MPs are demanding a police investigation into whether Russian money influenced the outcome of the Brexit referendum.

They have written to Cressida Dick, Commissioner of the Metropolitan Police, asking the force to investigate whether “money ultimately of a foreign origin” was routed into the EU referendum.

The letter was signed by 18 MPs including Liam Byrne, Labour MP for Birmingham Hodge Hill, and Shabana Mahmood, Labour MP for Birmingham Ladywood.

It follows reports that millionaire Arron Banks, who donated to unofficial Brexit campaign Leave.EU, had meetings with the Russian ambassador to Britain and visited Moscow at the height of the campaign.

Millionaire Brexit campaigner Arron Banks

The letter said: “We write to ask that consider opening investigations alongside the Electoral Commission into possible offences by Leave.EU under the Political Parties, Elections and Referendums Act, 2000, specifically the routing of money ultimately of a foreign origin into the recent referendum on membership of the European Union, in contravention of the law that donations may only be made by a permissible source.”

Mr Banks, a former Ukip donor, gave £9 million to the Leave.EU and Grassroots Out Brexit campaigns, mostly in the form of loans and branded merchandise.

Leave.EU was an unofficial campaign during the 2016 EU referendum. It was supported by former UKIP leader Nigel Farage and highlighted the issue of immigration.

The official Vote Leave campaign, supported by Boris Johnson, focused more on the cost of EU membership.

Leaked emails have revealed that Mr Banks held three meetings with Russian ambassador Alexander Yakovenko.

Shabana Mahmood, Labour MP for Birmingham Ladywood

Mr Banks had previously claimed he met the ambassador only once, at a “six-hour boozy lunch”.

But it has emerged that along with his right hand man Andy Wigmore he had two further meetings with the ambassador. Mr Banks also visted Moscow in February 2016, as the referendum campaign was under way.

Mr Banks denies there is anything to investigate regarding his donations - but has asked the police to investigate what he calls the theft of the emails.

Mr Banks and Andrew Wigmore, a businessman who worked with him on the Brexit campaign, said in a statement: “We have reported the theft of material belonging to us – which we are led to believe was stolen from the journalist Isabel Oakeshott – to the police.

“Isabel Oakeshott used the original material to help co-write the book, ‘The Bad Boys of Brexit’.

“Misleading and incorrect stories based on limited information have appeared in the Guardian and Observer who say they had seen these emails from a source.”

They went on to say: “We have reported the theft of our material to Avon & Somerset and Thames Valley police.”